Deleting contacts from iMessage (Not contacts)

So to delete a contact I’d go to contacts, find the contact I want to remove, select it then hit edit at the top right. I scroll down and hit delete.

Theres times I’m going through iMessages and I realize I’d like to delete a contact or multiple. So as an easy step, to scroll through iMessage, (since I’m already there) identify who I want to remove (perhaps it’s someone I havn’t talked to in a while) I hit the info contacts circle at the top of the message, select the info button, then edit at the top right. However the delete contact button isn’t here.

Am I missing something? This seems like an oversight at some capacity.